2000 年度実績報告書

時間遅れを含む数理生物モデルのパーシステンスとカオス

研究課題

研究課題/領域番号	09640256
研究機関	静岡大学
研究代表者	竹内康博静岡大学, 工学部, 教授 (20126783)
キーワード	数理生物モデル / パーシステンス / カオス / 時間遅れ
研究概要	本研究の目的は数理生物学において基本的な概念であるパーシステンスが時間遅れの導入によりどのような影響を受けるかを調べるとともに,カオス現象を解析し,時間遅れをもった数理生物モデルの解析手法を確立することである.特に(1)生物の増殖プロセスと物質のリサイクリングプロセスに時間遅れを導入したケモスタットモデル;(2)伝染病の非感染者が保菌者から感染者に移行するプロセスに時間遅れを考慮した疫学モデル;(3)赤血球に薬物を閉じこめて患者に注射し,マクロファージが赤血球を食するための時間遅れを利用して薬物の投与効果を長時間持続させる医学上の方法についてのモデルを考察する. 上記数理モデルのパーシステンスに対する時間遅れの影響をまとめ,時間遅れをもった数理生物モデルの大域的安定性解析手法を確立した.具体的な研究実績の概要は以下の通りであった. 1.モデル(3)で、薬物の効果が長く持続するような赤血球の齢分布を決定した(11の論文2). 2.差分・微分不等式を証明し、非線形の遅れ型・中立型関数微分方程式系の安定性解析に応用した(論文3,4,6).特に遅れ型を中立型に変換し安定性解析を見通しよくし、個体群力学系を解析した(論文1,7,8). 3.上記2の方法をモデル(2)の解析に用い(論文5,9),さらに拡張したモデル(2)に適用した(論文10,11,20). 4.同手法を2つのニューロンをもつニューラルネットワークに適用し、その安定性に対する時間遅れの影響を考察した(論文12). 5.個体群力学系における数理モデル(差分方程式系)の動的挙動を解析し、カオス発生条件およびその進化に対する影響を考察し、系が安定系からカオス系に進化することを示した(論文14,18). 6.時間遅れを持つ微分方程式系が周期解を持たない条件を求めた(論文15-17). 7.上記モデルとは別に環境ホルモンの生物種成長への影響を考察するために時間遅れモデルを提案し,そのパーシステンスと安定性を解析した(論文19). 8.また格子モデルにおけるパーシステンスとカタストロフィーについて考察した(論文13,19).

研究成果

(21件)

すべてその他

すべて文献書誌 (21件)

[文献書誌] J. Hofbauer.: "Global stability of competition in a spatially heterogeneous environment"Differential Equations and Dynamical Systems. 4・2. 213-223 (1996)
[文献書誌] E.Beretta: "A mathematical model for drug administration by using the phagocytosis of red blood cells"J.Math.Biol.. 35. 1-19 (1996)
[文献書誌] W.Ma: "Instability analysis of nonlinear neutral differential difference systems with infinite delays"Dynamics of Continuous, Discrete and Impulsive Systems. 2・4. 437-460 (1996)
[文献書誌] W.Ma: "A nonlinear differential difference inequality and instability analysis of nonlinear retarded differential large scale systems with infinite delays"Nonlinear World. 3. 643-664 (1996)
[文献書誌] E.Beretta: "Convergence results in SIR epidemic models with varying population size"Nonlinear Analysis, Theory, Methods and Applications. 28・12. 1909-1921 (1997)
[文献書誌] W.Ma: "Stability of neutral differential difference systems with infinite delays"Nonlinear Analysis, Theory, Methods and Applications. 33・4. 367-390 (1998)
[文献書誌] Y.Takeuchi: "Global attractivity of mixed Lotka-Volterra differential systems with delays"Canadian Applied Mathematics Quarterly. 6・3. 245-267 (1998)
[文献書誌] W.Ma: "Stability analysis on a predator-prey system with distributed delays"J.Computational and Applied Mathematics. 88. 79-94 (1998)
[文献書誌] Y.Takeuchi: "Delay effect on the threshold properties of SIR epidemic models"Adavanced Topics in Biomathematics. 247-252 (1998)
[文献書誌] Y.Takeuchi: "Stability analysis on a delayed SIR epidemic model with density dependent birth process"Dynamics of Continuous,Discrete and Impulsive Systems. 5・1-4. 171-184 (1999)
[文献書誌] Y.Takeuchi: "Global asymptotic properties of a delay SIR epidemic model with varying population size and finite incubation times"Nonlinear Analysis, Theory, Methods and Applications. 42・6. 931-947 (2000)
[文献書誌] W.Ma: "Stability of a 2-dimensional neural network with time delays"J.Biological Systems. 8・2. 177-193 (2000)
[文献書誌] K.Tainaka,: "Dynamic Process and variation in the contact process"Physics Letters A. 272. 416-420 (2000)
[文献書誌] R.Kon: "The effect of evolution on host-parasitoid systems"J.Theoretical Biology. (印刷中).
[文献書誌] E.Beretta: "Nonexistence of periodic solutions in a class of delay-differential equations"Proceeding of Atlanta Conf. (印刷中).
[文献書誌] E.Beretta: "Non-existence of periodic solutions in delayed Lotka-Volterra systems"Nonlinear Analysis, Theory, Methods and Applications. (印刷中).
[文献書誌] E.Beretta: "Negative criteria for the existence of periodic solutions in class of delay-differential equations"Nonlinear Analysis, Theory, Methods and Applications. (印刷中).
[文献書誌] R.Kon: "Permanence of host-parasitoid systems"Nonlinear Analysis, Theory, Methods and Applications. (印刷中).
[文献書誌] Bo.Feng: "A stage-structured time-delay model of single-species exposed to environmental hormone"Nonlinear Analysis, Theory, Methods and Applications. (印刷中).
[文献書誌] E.Beretta: "Global asymptotic stability of an SIR epidemic model with distributed time delay"Nonlinear Analysis, Theory, Methods and Applications. (印刷中).
[文献書誌] K.Tainaka: "Spatial pattern formation in a model ecosystem : exchange between symbiosis and competition"Physics Letters A. (印刷中).

2000 年度 実績報告書

時間遅れを含む数理生物モデルのパーシステンスとカオス

研究代表者

竹内 康博 静岡大学, 工学部, 教授 (20126783)

研究成果

[文献書誌] J. Hofbauer.: "Global stability of competition in a spatially heterogeneous environment"Differential Equations and Dynamical Systems. 4・2. 213-223 (1996)

[文献書誌] E.Beretta: "A mathematical model for drug administration by using the phagocytosis of red blood cells"J.Math.Biol.. 35. 1-19 (1996)

[文献書誌] W.Ma: "Instability analysis of nonlinear neutral differential difference systems with infinite delays"Dynamics of Continuous, Discrete and Impulsive Systems. 2・4. 437-460 (1996)

[文献書誌] W.Ma: "A nonlinear differential difference inequality and instability analysis of nonlinear retarded differential large scale systems with infinite delays"Nonlinear World. 3. 643-664 (1996)

[文献書誌] E.Beretta: "Convergence results in SIR epidemic models with varying population size"Nonlinear Analysis, Theory, Methods and Applications. 28・12. 1909-1921 (1997)

[文献書誌] W.Ma: "Stability of neutral differential difference systems with infinite delays"Nonlinear Analysis, Theory, Methods and Applications. 33・4. 367-390 (1998)

[文献書誌] Y.Takeuchi: "Global attractivity of mixed Lotka-Volterra differential systems with delays"Canadian Applied Mathematics Quarterly. 6・3. 245-267 (1998)

[文献書誌] W.Ma: "Stability analysis on a predator-prey system with distributed delays"J.Computational and Applied Mathematics. 88. 79-94 (1998)

[文献書誌] Y.Takeuchi: "Delay effect on the threshold properties of SIR epidemic models"Adavanced Topics in Biomathematics. 247-252 (1998)

[文献書誌] Y.Takeuchi: "Stability analysis on a delayed SIR epidemic model with density dependent birth process"Dynamics of Continuous,Discrete and Impulsive Systems. 5・1-4. 171-184 (1999)

[文献書誌] Y.Takeuchi: "Global asymptotic properties of a delay SIR epidemic model with varying population size and finite incubation times"Nonlinear Analysis, Theory, Methods and Applications. 42・6. 931-947 (2000)

[文献書誌] W.Ma: "Stability of a 2-dimensional neural network with time delays"J.Biological Systems. 8・2. 177-193 (2000)

[文献書誌] K.Tainaka,: "Dynamic Process and variation in the contact process"Physics Letters A. 272. 416-420 (2000)

[文献書誌] R.Kon: "The effect of evolution on host-parasitoid systems"J.Theoretical Biology. (印刷中).

[文献書誌] E.Beretta: "Nonexistence of periodic solutions in a class of delay-differential equations"Proceeding of Atlanta Conf. (印刷中).

[文献書誌] E.Beretta: "Non-existence of periodic solutions in delayed Lotka-Volterra systems"Nonlinear Analysis, Theory, Methods and Applications. (印刷中).

[文献書誌] E.Beretta: "Negative criteria for the existence of periodic solutions in class of delay-differential equations"Nonlinear Analysis, Theory, Methods and Applications. (印刷中).

[文献書誌] R.Kon: "Permanence of host-parasitoid systems"Nonlinear Analysis, Theory, Methods and Applications. (印刷中).

[文献書誌] Bo.Feng: "A stage-structured time-delay model of single-species exposed to environmental hormone"Nonlinear Analysis, Theory, Methods and Applications. (印刷中).

[文献書誌] E.Beretta: "Global asymptotic stability of an SIR epidemic model with distributed time delay"Nonlinear Analysis, Theory, Methods and Applications. (印刷中).

[文献書誌] K.Tainaka: "Spatial pattern formation in a model ecosystem : exchange between symbiosis and competition"Physics Letters A. (印刷中).

2000 年度実績報告書

竹内康博静岡大学, 工学部, 教授 (20126783)